Problem: Ikta has an extraordinary feeling for undirected graphs. Ikta likes the undirected graph G and its two-point s, t pair (G, s, t) that has the greatest "beauty". The "beauty" of a pair (G, s, t) is the edge e = \\ {u, v \\} (u and v are two different points of G), and the shortest path from s to t in G. Is the number of things whose length is greater than the length of the shortest path from s to t in the undirected graph with g plus e.

Your job is to write a program that seeks its "beauty" given a pair (G, s, t).



Input

The input is given in the following format.

> N M s t
> x1 y1
> ...
> xi yi
> ...
> xM yM
>

First, the number of vertices, the number of edges, and the integers N, M, s, t representing the two vertices of the undirected graph are input. From the 2nd line to the M + 1th line, two vertices connected by edges are input. (However, let the set of G vertices be \\ {1, ..., N \\}.)

Constraints

Each variable being input satisfies the following constraints.

* 2 ≤ N ≤ 100,000
* 1 ≤ M ≤ 300,000
* 1 ≤ s, t, xi, yi ≤ N
* Different from s and t
* Guaranteed to reach t from s

Output

When the given graph is G, output the "beauty" of the set (G, s, t) in one line.

Examples

Input

3 2 1 3
1 2
2 3


Output

1


Input

9 8 7 8
2 6
4 9
8 6
9 2
3 8
1 8
8 5
7 9


Output

7


Input

4 3 1 4
1 2
3 4
4 1


Output

0


Input

9 7 8 9
9 6
6 5
3 6
3 7
2 5
8 5
1 4


Output

2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rep1(i, n) for (int i = 1; i < (n); i++)
#define all(v) (v).begin(), (v).end()
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
using namespace std;
typedef long long LL;
const int INF = 999999999;

struct edge{
    int src, to, cost;
};
using Edges = vector<edge>;
using WeightedGraph = vector<Edges>;

vector<int> dijkstra(WeightedGraph &G, int st){
    vector<int> dist(G.size(), INF);
    using pi = pair<int, int>;
    priority_queue<pi, vector<pi>, greater<pi>> q;
    dist[st] = 0;
    q.push(mp(dist[st], st));
    while(!q.empty()){
        int cost, idx;
        tie(cost, idx) = q.top(); q.pop();
        if(dist[idx] < cost) continue;
        for(auto &e: G[idx]){
            if(dist[e.to] <= cost+e.cost) continue;
            dist[e.to] = cost+e.cost;
            q.push(mp(dist[e.to], e.to));
        }
    }
    return dist;
}

int main(){
    int N, M, s, t;
    cin >> N >> M >> s >> t;
    s--; t--;
    WeightedGraph G(N);
    rep(i, M){
        int x, y;
        cin >> x >> y;
        x--; y--;
        G[x].emplace_back((edge){x, y, 1});
        G[y].emplace_back((edge){y, x, 1});
    }
    vector<int> ds, dt;
    ds = dijkstra(G, s);
    dt = dijkstra(G, t);
    int X = ds[t];
    map<int, int> ms, mt;
    rep(i, N){
        ms[ds[i]]++;
        mt[dt[i]]++;
    }

    LL ans = 0;
    for(auto &i: ms){
        int tmp = X-2-i.first;
        ans += 1LL*i.second*mt[tmp];
    }
    cout << ans << endl;
}